Abstract
SetS inR d has propertyK 2 if and only ifS is a finite union ofd-polytopes and for every finite setF in bdryS there exist points c1,c2 (depending onF) such that each point ofF is clearly visible viaS from at least one ci,i = 1,2. The following characterization theorem is established: Let\(S \subseteq R^d\), d≠2. SetS is a compact union of two starshaped sets if and only if there is a sequence {S j } converging toS (relative to the Hausdorff metric) such that each setS j satisfies propertyK 2. For\(S \subseteq R^2\), the sufficiency of the condition above still holds, although the necessity fails.
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Breen, M. Characterizing compact unions of two starshaped sets inR d . J Geom 35, 14–18 (1989). https://doi.org/10.1007/BF01222257
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DOI: https://doi.org/10.1007/BF01222257